Reflection Groups and Coxeter Groups

  • Alexandre V. Borovik
  • I. M. Gelfand
  • Neil White
Chapter
Part of the Progress in Mathematics book series (PM, volume 216)

Abstract

This chapter is of an auxiliary nature and contains the modicum of the theory of finite reflection groups and Coxeter groups which we need for a systematic development of the theory of Coxeter matroids. A reflection group W is a finite subgroup of the orthogonal group of ℝ n generated by some reflections in hyperplanes (mirrors or walls). The mirrors cut ℝ n into open polyhedral cones, called chambers. The geometric concepts associated with the resulting chamber system (called the Coxeter complex of W) form the language of the theory of Coxeter matroids. The reader familiar with the theory of reflection groups and Coxeter groups may skip most of the chapter. However, we recommend that this reader look through Sections 5.12 “Residues,” 5.14 “Bruhat order” and 5.15 “Splitting the Bruhat order.”

Keywords

Assure Hull Sp41 

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Copyright information

© Birkhäuser Boston 2003

Authors and Affiliations

  • Alexandre V. Borovik
    • 1
  • I. M. Gelfand
    • 2
  • Neil White
    • 3
  1. 1.Department of MathematicsUMISTManchesterUK
  2. 2.Department of MathematicsRutgers UniversityPiscatawayUSA
  3. 3.Department of MathematicsUniversity of FloridaGainesvilleUSA

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